The Wentzel–Kramers–Brillouin (WKB) method is one of the main tools in quantum mechanics and quantum field theory. From the mathematical point of view, this method coincides with construction of asymptotic expansions for a solution to the second-order differential equations with a small coefficient of the second derivative term . In the present work, we consider an interesting modification of the WKB method – the so-called method of comparison equations and analyze its relation with the Ermakov equation..
A.Y. Kamenshchik, M. Luzzi, G. Venturi (2009). METHOD OF COMPARISON EQUATIONS AND GENERALIZED ERMAKOV’S EQUATION. RUSSIAN PHYSICS JOURNAL, 52, 1339-1351 [10.1007/s11182-010-9375-4].
METHOD OF COMPARISON EQUATIONS AND GENERALIZED ERMAKOV’S EQUATION
KAMENCHTCHIK, ALEXANDR;LUZZI, MATTIA;VENTURI, GIOVANNI
2009
Abstract
The Wentzel–Kramers–Brillouin (WKB) method is one of the main tools in quantum mechanics and quantum field theory. From the mathematical point of view, this method coincides with construction of asymptotic expansions for a solution to the second-order differential equations with a small coefficient of the second derivative term . In the present work, we consider an interesting modification of the WKB method – the so-called method of comparison equations and analyze its relation with the Ermakov equation..I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
